Quantitative Techniques for Business.pdf PDF

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QUANTITATIVE TECHNIQUES FOR BUSINESS (BCM4C04)

STUDY MATERIAL COMPLEMENTARY COURSE

IV SEMESTER

B.Com. (2019 Admission)

UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION CALICUT UNIVERSITY P.O. MALAPPURAM - 673 635, KERALA

19612

School of Distance Education University of Calicut Study Material : IV Semester B.Com. (2019 Admission) Complementary Course : BCM4C04 QUANTITATIVE TECHNIQUES FOR BUSINESS Prepared by:

Modules I-IV Sri. VINEETHAN T. Assistant Professor, Dept. of Commerce Govt. College, Madappally. Module V Sri. RAJAN P.. Assistant Professor of Commerce School of Distance Education, University of Calicut. Scrutinized by:

Modules I-IV Dr. K. VENUGOPALAN Associate Professor, Dept. of Commerce Govt. College, Madappally. Module V Sri. MUHAMMED FAISAL T. Asst. Professor of Commerce EMEA College of Arts & Science, Kondotty.

DISCLAIMER "The author(s) shall be solely responsible for the content and views expressed in this book".

Printed @ Calicut University Press

CONTENTS Module

Title

Page No.

1

Quantitative Techniques

1-8

2

Correlation and Regression Analysis

9-56

3

Set Theory

57-88

4

Theoretical Distribution

89-121

5

Quantitative Approaches to Decision Making

122-151

BCM4C04: Quantitative Techniques for Business

Module I QUANTITATIVE TECHNIQUES Meaning and Definition Quantitative techniques may be defined as those techniques which provide the decision makes a systematic and powerful means of analysis, based on quantitative data. It is a scientific method employed for problem solving and decision making by the management. With the help of quantitative techniques, the decision maker is able to explore policies for attaining the predetermined objectives. In short, quantitative techniques are inevitable in decision-making process. Classification of Quantitative Techniques There are different types of quantitative techniques. We can classify them into three categories. They are: 1. 2. 3.

Mathematical Quantitative Techniques Statistical Quantitative Techniques Programming Quantitative Techniques

Mathematical Quantitative Techniques A technique in which quantitative data are used along with the principles of mathematics is known as mathematical quantitative techniques. Mathematical quantitative techniques involve: 1.

Permutations and Combinations

Permutation means arrangement of objects in a definite order. The number of arrangements depends upon the total number of objects and the number of objects taken at a time for arrangement. The number of permutations or arrangements is calculated by using the following formula:-

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BCM4C04: Quantitative Techniques for Business

n Pr 

n! n  r !

Combination means selection or grouping objects without considering their order. The number of combinations is calculated by using the following formula:-

n Cr  2.

n!  n  r !

Set Theory

Set theory is a modern mathematical device which solves various types of critical problems. 3.

Matrix Algebra

Matrix is an orderly arrangement of certain given numbers or symbols in rows and columns. It is a mathematical device of finding out the results of different types of algebraic operations on the basis of the relevant matrices. 4.

Determinants:

It is a powerful device developed over the matrix algebra. This device is used for finding out values of different variables connected with a number of simultaneous equations. 5.

Differentiation

It is a mathematical process of finding our changes in the dependent variable with reference to a small change in the independent variable. 6.

Integration Integration is the reverse process of differentiation.

7.

Differential Equation

It is a mathematical equation which involves the differential coefficients of the dependent variables. School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

Statistical Quantitative Techniques Statistical techniques are those techniques which are used in conducting the statistical enquiry concerning to certain Phenomenon. They include all the statistical methods beginning from the collection of data till interpretation of those collected data. Statistical techniques involve: 1.

Collection of data One of the important statistical methods is collection of data. There are different methods for collecting primary and secondary data. 2. Measures of Central tendency, dispersion, skewness and Kurtosis Measures of Central tendency is a method used for finding he average of a series while measures of dispersion used for finding out the variability in a series. Measures of Skewness measures asymmetry of a distribution while measures of Kurtosis measures the flatness of peakedness in a distribution. 3.

Correlation and Regression Analysis Correlation is used to study the degree of relationship among two or more variables. On the other hand, regression technique is used to estimate the value of one variable for a given value of another. 4.

Index Numbers Index numbers measure the fluctuations in various Phenomena like price, production etc over a period of time. They are described as economic barometres. 5.

Time Series Analysis Analysis of time series helps us to know the effect of factors which are responsible for changes: School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

6.

Interpolation and Extrapolation

Interpolation is the statistical technique of estimating under certain assumptions, the missing figures which may fall within the range of given figures. Extrapolation provides estimated figures outside the range of given data. 7.

Statistical Quality Control

Statistical quality control is used for ensuring the quality of items manufactured. The variations in quality because of assignable causes and chance causes can be known with the help of this tool. Different control charts are used in controlling the quality of products. 8.

Ratio Analysis

Ratio analysis is used for analyzing financial statements of any business or industrial concerns which help to take appropriate decisions. 9.

Probability Theory

Theory of probability provides numerical values of the likely hood of the occurrence of events. 10.

Testing of Hypothesis

Testing of hypothesis is an important statistical tool to judge the reliability of inferences drawn on the basis of sample studies. Programming Techniques Programming techniques are also called operations research techniques. Programming techniques are model building techniques used by decision makers in modern times. Programming techniques involve: 1.

Linear Programming Linear programming technique is used in finding a

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BCM4C04: Quantitative Techniques for Business

solution for optimizing a given objective under certain constraints. 2.

Queuing Theory Queuing theory deals with mathematical study of queues. It aims at minimizing cost of both servicing and waiting. 3. Game Theory Game theory is used to determine the optimum strategy in a competitive situation. 4.

Decision Theory This is concerned with making sound decisions under conditions of certainty, risk and uncertainty. 5.

Inventory Theory Inventory theory helps for optimizing the inventory levels. It focuses on minimizing cost associated with holding of inventories. 6. Net work programming It is a technique of planning, scheduling, controlling, monitoring and co-ordinating large and complex projects comprising of a number of activities and events. It serves as an instrument in resource allocation and adjustment of time and cost up to the optimum level. It includes CPM, PERT etc. 7.

Simulation It is a technique of testing a model which resembles a real life situations. 8.

Replacement Theory It is concerned with the problems of replacement of machines, etc due to their deteriorating efficiency or breakdown. It helps to determine the most economic replacement policy. School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

9.

Non Linear Programming

It is a programing technique which involves finding an optimum solution to a problem in which some or all variables are non-linear. 10.

Sequencing Sequencing tool is used to determine a sequence in which given jobs should be performed by minimising the total efforts. 11.

Quadratic Programming

Quadratic programming technique is designed to solve certain problems, the objective function of which takes the form of a quadratic equation. 12.

Branch and Bound Technique

It is a recently developed technique. This is designed to solve the combinational problems of decision making where are large number of feasible solutions. Problems of plant location, problems of determining minimum cost of production etc. are examples of combinational problems. Functions of Quantitative Techniques The following are quantitative techniques.

the

important functions of

1.

To facilitate the decision-making process

2.

To provide tools for scientific research

3.

To help in choosing an optimal strategy

4.

To enable in proper deployment of resources

5.

To help in minimizing costs

6.

To help in minimizing the total processing time required for performing a set of jobs. USES OF QUANTITATE TECHNIQUES

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BCM4C04: Quantitative Techniques for Business

Business and Industry Quantitative techniques render valuable services in the field of business and industry. Today, all decisions in business and industry are made with the help of quantitative techniques. Some important uses of quantitative techniques in the field of business and industry are given below: 1. Quantitative techniques of linear programming is used for optimal allocation of scarce resources in the problem of determining product mix. 2. Inventory control techniques are useful in dividing when and how much items are to be purchase so as to maintain a balance between the cost of holding and cost of ordering the inventory. 3. Quantitative techniques of CPM, and PERT helps in determining the earliest and the latest times for the events and activities of a project. This helps the management in proper deployment of resources. 4. Decision tree analysis and simulation technique help the management in taking the best possible course of action under the conditions of risks and uncertainty. 5. Queuing theory is used to minimize the cost of waiting and servicing of the customers in queues. 6. Replacement theory helps the management of determining the most economic replacement policy regarding replacement of an equipment. Limitations of Quantitative Techniques Even though the quantitative techniques are inevitable in decision-making process, they are not free from short comings. The following are the important limitations of quantitative techniques. 1. Quantitative techniques involves mathematical models, equations and other mathematical expressions. School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

2. Quantitative techniques are based on number of assumptions. Therefore, due care must be ensured while using quantitative techniques, otherwise it will lead to wrong conclusions. 3. Quantitative techniques are very expensive. 4. Quantitative techniques do not take into consideration intangible facts like skill, attitude etc. 5. Quantitative techniques are only tools for analysis and decision-making. They are not decisions itself.

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BCM4C04: Quantitative Techniques for Business

Module 2 CORRELATION ANALYSIS Introduction In practice, we may come across with lot of situations which need statistical analysis of either one or more variables. The data concerned with one variable only is called univariate data. For Example: Price, income, demand, production, weight, height marks etc are concerned with one variable only. The analysis of such data is called univariate analysis. The data concerned with two variables are called bivariate data. For example: rainfall and agriculture; price and demand; height and weight etc. The analysis of these two sets of data is called bivariate analysis. The date concerned with three or more variables are called multivariate data. For example; agricultural production is influenced by rainfall, quality of soil, fertilizer etc. The statistical technique which can be used to study the relationship between two or more variables is called correlation analysis. Definition Two or more variables are said to be correlated if the change in one variable results in a corresponding change in the other variable. According to Simpson and Kafka, "Correlation analysis deals with the association between two or more variables". Lun Chou defines, "Correlation analysis attempts to determine the degree of relationship between variables". Boddington states that "Whenever some definite connection exists between two or more groups or classes of School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

series of data, there is said to be correlation". In nut shell, correlation analysis is an analysis which helps to determine the degree of relationship exists between two or more variables. Correlation Coefficient Correlation analysis is actually an attempt to find a numerical value to express the extent of relationship exists between two or more variables. The numerical measurement showing the degree of correlation coefficient. Correlation coefficient ranges between-1 and +1. SIGNIFICANCE OF CORRELATION ANALYSIS Correlation analysis is of immense use in practical life because of the following reasons: 1.

Correlation analysis helps us to find a single figure to measure the degree of relationship exists between the variables.

2.

Correlation analysis helps to understand the economic behavior.

3.

Correlation analysis enables the business executives to estimate cost, price and other variables. Correlation analysis can be used as a basis for the study of regression. Once we know that two variables are closely related, we can estimate the value of one variable if the value of other is known.

4.

5.

Correlation analysis helps to reduce the range of uncertainty associated with decision making. The prediction based on correlation analysis is always near to reality.

6.

It helps to know whether the correlation is significant or not. This is possible by comparing the correlation

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BCM4C04: Quantitative Techniques for Business

co-efficient with 6PE. It 'r' is more than 6 PE, the correlation is significant. Classification of Correlation Correlation can be classified in different ways. The following are the most important classifications. 1. Positive and Negative correlation 2.

Simple, partial and multiple correlation

3.

Linear and Non-linear correlation

Positive and Negative Correlation Positive Correlation When the variables are varying in the same direction, it is called positive correlation. In other words, if an increase in the value of one variable is accompanied by an increase in the value of other variable or if a decrease in the value of one variable is accompanied by a decree se in the value of other variable, it is called positive correlation. Eg:

1) A: 10 B: 80 2) X: 78 Y: 20

20

30

40

50

100

150

170

200

60 18

52 14

46 10

38 5

Negative Correlation When the variables are moving in opposite direction, it is called negative correlation. In other words, if an increase in the value of one variable is accompanied by a decrease in the value of other variable of if a decrease in the value of one variable is accompanied by an increase in the value of other variable, it is called negative correlation.

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BCM4C04: Quantitative Techniques for Business

Eg: 1) A:

5

10

15

20

25

B:

16

10

8

6

2

2) X:

40

32

25

20

10

Y:

2

3

5

8

12

Simple, Partial and Multiple Correlation Simple Correlation In a correlation analysis, if only two variables are studied it is called simple correlation. Eg. the study of the relationship between price & demand, of a product or price and supply of a product is a problem of simple correlation. Multiple correlation In a correlation analysis, if three or more variables are studied simultaneously, it is called multiple correlation. For example, when we study the relationship between the yield of rice with both rainfall and fertilizer together, it is a problem of multiple correlation. Partial correlation In a correlation analysis, we recognize more than two variable, but consider one dependent variable and one independent variable and keeping the other Independent variables as constant. For example yield of rice is influenced by the amount of rainfall and the amount of fertilizer used. But if we study the correlation between yield of rice and the amount of rainfall by keeping the amount of fertilizers used as constant, it is a problem of partial correlation. Linear and Non-linear correlation Linear Correlation In a correlation analysis, if the ratio of change between the two sets of variables is same, then it is called linear correlation. School of Distance Education, University of Calicut

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BCM4C04: Quantitative Techniques for Business

For examples when 10% increase in one variable is accompanied by 10% increase in the other variable, it is the problem of linear correlation. X:

10

15

30

60

Y:

50

75

150

300

Here the ratio of change between X and Y is the same. When we plot the data in graph paper, all the plotted points would fall on a straight line. Non-linear correlation In a correlation analysis if the amount of change in one variable does not bring the same ratio of change in the other variable, it is called non linear correlation. X:

2

4

6

10

15

Y:

8

10

18

22

26
...